Question 168 of 191

Unpolarised light of intensity $32W{m}^{-2}$ passes through the combination of three polaroids such that the pass axis of the last polaroids is perpendicular to that of the pass axis of first polaroids. If intensity of emerging light is $3W{m}^{-2}$, then the angle between pass axis of first two polaroids is _________$^{\circ}$.

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Answer: 30

The given data is
${I}_{0}=32W{m}^{-2}$
${I}_{f}=3W{m}^{-2}$
Thus, by substituting the value, we get
${I}_{f}=\left(\dfrac{{I}_{0}}{2}{\cos }^{2}\theta \right)\times {\cos }^{2}\left(90^{\circ}-\theta \right)...(i)$
$\Rightarrow 3=16\left({\cos }^{2}\theta \cdot {\sin }^{2}\theta \right)$
$\Rightarrow \cos \theta \cdot \sin \theta =\dfrac{\sqrt{3}}{4} \Rightarrow \sin 2\theta =\dfrac{\sqrt{3}}{2} \Rightarrow \theta =30^{\circ}$